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Large deviations for estimators of unknown probabilities, with applications in risk theory

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  • Macci, Claudio

Abstract

We present large deviation results for estimators of unknown probabilities which satisfy a suitable exponential decay condition. These results provide some extensions of the large deviation estimates given in Macci and Petrella (2006). Furthermore we propose a classical approach which is different from the one presented in Ganesh et al. (1998) and we cannot say that the Bayesian approach is more conservative as in that paper.

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  • Macci, Claudio, 2011. "Large deviations for estimators of unknown probabilities, with applications in risk theory," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 16-24, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:16-24
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    References listed on IDEAS

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    1. Avram, Florin & Palmowski, Zbigniew & Pistorius, Martijn, 2008. "A two-dimensional ruin problem on the positive quadrant," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 227-234, February.
    2. Claudio Macci, 2010. "Large deviations for estimators of some threshold parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(1), pages 63-77, March.
    3. Ganesh, Ayalvadi & O'Connell, Neil, 1999. "An inverse of Sanov's theorem," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 201-206, April.
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    Cited by:

    1. Claudio Macci & Stefano Trapani, 2013. "Large deviations for posterior distributions on the parameter of a multivariate $$\text{ AR}(p)$$ process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 703-719, August.

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